Article #288
Subject: How the definition of motion relates to Dr. Adler's proof of God's existence
Author: Andrew W. Harrell
Posted: 7/12/2016 11:38:41 AM

I remember sending Dr. Adler a request when I was 10 years old and working on a science fair project or
so for information on how to relate the temperature to the number of cricket chips per minute. He has
offered to do two literature research on any topic for anyone who had bought a set of his Enclopedia
Britanicas. My mother remembered him as teaching my Uncle at the U. of Chicago in the 1930s and had
bought a set. Mortimer sent me about 20 pages of information on this topic. It really meant a lot to me
for I was able to win a district award with my project.
Some years later I did a project on training Planaria worms with electric shocks and them cutting them
in two and testing them after they grew back the other halfs of their bodies to see if they still
remembered there training equally in the head and torso parts. He also sent me information on this.
With this project I made it to the state science fair competition and placed second, which helped me win
a half scholarship to Vanderbilt.
About ten years later I had a doctorate in mathematics from UC Berkekey and while working in
Washington DC was listening to his interviews with Mr. Buckley [whom I also met while taking
philosophy cours as an undergraduate at Vanderbilt] I got interested in learning the details of his proof
that God existed. I never knew my father, Judson Gordon Harrell much, who was the son of a famous
Christian Evangelist. But, one thing he had said to me with quite a lot of certainity was, “You cannot
prove that God exists.”
I wrote Dr. Adler my thoughts on his proof. He never answered that letter, but being the Angel he is, he
appeared to me in a dream and said ‘You need to study and explain to me how motion is defined in
order to carry through with your arguments and understand mine better.”
So when I visited the Galileo museum in Florence last year and wrote my thoughts down for a short
review of the book


From the http://www.ourprayergroup.blogspot.com May 2015 posting:


Discussion of the importance of Galileo’s life and work to modern science and philosophy and theology,
as part of a review of the overall Church’s (Catholic, Protestant, Jewish, Hindu) perspective on his life
700 years later.

References:
Galileo by J.L.Heibron Oxford U. Press
(See the May 2015 issue of the American Mathematical Society (AMS) Notices for a review by
mathematicians...not necessarily theologians...of this recently published book. Unfortunately not many
of our prominent mathematicians today believe it is possible to be both a mathematician and a
theologian like Galileo was, [and still is]. Last year after being asked to donate a brick to the
Mathematical Association of America (MAA) I sent in some money and the following inscription to be
placed on the brick "When God is One, His Truth is One, YHWH Christ". Some weeks later I received a
letter from the MAA board saying they had voted and that inscription would not be acceptable for a
commemorative brick to be placed at the headquarters.)
see also

Lectures on Thought and Effort by L. Ron Hubbard, 1953. Mr. Hubbard defines motion as "change of
place and attitude." Which is a definition combining the distinctions referred to below that Aristotle
made between types of local and general motion.

The Trial of Galileo, Aristotelianism, the “New Cosmology,” and the Catholic Church, 1616-1633 by
Michael S. Pettersen, Frederick Purnell,Mark Carnes
[

Galileo, along with Aristotle, was and still is, one of the most important thinkers in the area of
mathematics, theology, and physics the human race has produced, He is responsible for not only
helping us get rid of an earth centered view of the solar system and an over dependence and
acceptance of science and religion upon unchallenged tradition ideas, but also reframing the actual
ways and methods science and religion helps us to improve itself by knowing new ideas and ideas
about ourselves and these ideas themselves. .
Just 15 years ago or so Pope John Paul II ordered a review of the Christian Church whole discussions
with and about Galileo. Although, not a Catholic, but a Protestant I take this as an opportunity for the
whole Church of believers in Christ [Catholic, Protestant, Jewish to reconsider things together about
these important subjects. And, also to encourage us to perhaps try and understand motion somewhat
better than Galileo did. Godel's incompleteness theorem proved that there are logical boundaries to
what we as humans and computers can understand or create. But, the more important truth is that
there are no logical limits to what computers and the human mind can understand or create, when we
put our computers and minds and the world together under the control of God.
When Galileo was a professor of mathematics and physics at Pisa much of the the way we understand
mathematics and physics now did not exist. Real numbers [roughly speaking limits of rational and
irrational numbers] which are the key to the way we understand how to use Calculus to study physics
weren’t defined yet. Galileo couldn't use the ratios of time over space to define velocities as we do
nowadays.* This was because according to Euclid you could only measure ratios involving quantities of
the same type, like distance over distance or time over time. When he conducted the experiments
necessarily to determine a formula to represent the path of objects in free all or propelled from a
cannon he had to use Euclid axioms and Eudoxian proportion theory along with complicated theorems
on mean proportionals and over different types of combinations of different proportions. Decimal
numbers had already been introduced as a way of improving on the abacus and Roman numerals.
Fibonacci, one of Galileo’s predecessors at Pisa, had explained how to add and subtract using large
decimal numbers. But no one understood how to use a measure of time to compute moving velocities
and accelerations more than by using approximately geometrical values. Parmendides and Plato and
the methods of using limits of areas to exhaust calculations of the areas had been discussed in the
past. For, Archimedes had already discovered the philosophy of limits of numbers and volumes of
objects.
Aristotle had defined motion as “any kind of change” and he defined local motion as “change of
position or locution”. Galileo did not change our understanding of the broader definition but he did
change it of what Aristotle called local motion. Nowadays, in addition to reviewing and evaluating the
correctness of Galileo's theological arguments we should benefit by reviewing again how he understood
then and what we can understand now what 'motion' is. We define motion in terms of functions from
the real line [or complex or quaternions spaces which are made up of axes or vector bundles of real
continua or real spaces] to the some similar "type" of real lines or continua. Of course, since he, like
[Plato, Aristotle, Parmenides and the ancient Greeks, didn't yet understand what a continua was and
how it is defined mathematically] we should be able now to define what we want to call motion better
than he did. A robot can use the monomial equations of algebraic geometry as data structures in order
to calculate using functions or mappings where to go. While thinking about this, one thought I had was
that we knowing what we know now about computer science and expert systems [see some of my
papers on this at the website] could define a concept of "psychological motion" [emotion] for a robot.
The 'places' as Dr. Grothendeick has taught us on a manifold or topos defined algebraic geometrically
are different than those that we define through Euclidean metric geometry and spatial Newtonian
knowledge given to us by assuming certain axioms considering Space to be an absolute flat [uncurved]
Newtonian manifold.
All movement in space and time occurs in what the Buddhists call the "form" realms. But, we know[or at
least i believe] that we can represent movement in the "formless realms" by represent objects that don't
occur in space and time [are eternal] in our consciousness. If you believe philosophically and
theologically , as I do, and a lot of recent scientific studies have confirmed that mind [intentional
consciousness] having intentions existing both inside of our own minds and outside of them, and matter
[ not intentional consciousness] can both be represented mentally, conceptually, them we should be
able to move "formless" objects in our mind thereby affecting "form" that exists outside of it. After all,
when we remove knowledge of forms from our minds there is always a little of it left inside of us all,
because in order to create the knowledge you have to represent it in us. Consider and thinking deeply
about all of this perhaps we can mathematically represent the movement of both object and mental
functions of them in something that mathematicians now call "categories" of thinking mathematically.
For, a long time in the last two centuries mathematicians tried to understand all of mathematics just in
terms of what we call "sets of objects". But, now most of us recognize we need to broaden our thinking
to include not only "sets of mathematical objects" but "categories of objects and functions[ arrows that
represent a " field" of movement of the objects from a particular point of view [ what is called a monad
having a slightly different definition in computer science and mathematics at the present time.."]

* See Stillman Drakes wonderful translation of Galileo's Two New Sciences, along with its historical
appendix for a more detailed explanation of what I am talking about here.

The motion I am talking about would take place in a 2nd level reasoning structure superimposed as an
algebraic place on the manifold. It would occur in either a 'top-down' movement from the assumption of
a 'final cause' or faith therein such as some current Prolog language interpreters do using backward
thinking unification of clauses. Or it would occur in a 'bottom-up' object oriented type of thinking or
movement in knowledge instantiation. Is it possible to combine these two types of thinking, the
scientific and the theological? Yes, it you arrange the assumptions and conclusions of the thinking
rules according what is called in computer science a topological sort algorithm and use the type of
'mixed-chaining' instantiation that I described in my paper written for the U.S.Army Conference on
Computing using an example from the Corps of Engineers Seattle District river-bar formation rules.
Since what a function is depends on the data structures we use to define its mapping, is using such an
artificial intelligence, functional consciousness, definition of motion going to teach us new physics like
Galileo was taught new physics when he improved on Aristotle's idea of what motion is?

Aristotle argued from logic that local motion was of three kinds: 1: linear, 2:circular, 3:mixed of linear
and circular. He said this motion occurred because of natural tendencies in the element themselves and
not because of acceleration of velocities of motion of bodies relative to each other represented as
being effected or caused by a “force field”.
Under these assumptions linear motion cannot occur naturally without some external agent impressing
itself on the elements that are moving. However, circular motion will continue to move indefinitely. In
fact it is the archetype of how we define "theologically" eternal movement as something that has an
"end"[a purpose] in a "beginning" and a "beginning"[continuation of itself] in an "end", like circles do.
And, under these assumptions because the nature of objects vary the natural speeds at which they fall
and rise should also vary.
Galileo argued from experiments that he conducted both linear and circular motion occur because of a
universal force (which Newton later defined using his universal coefficient of attraction) occurring at all
times between two bodies. He found by experiment (dropping objects from the tower of Pisa and
measuring the time it took them to reach the ground) that heavier objects do not fall more quickly than
lighter ones. From this we can conclude that the acceleration of their velocities is a constant and it was
this constant that Newton later measured more precisely.

Newton, however, did not understand how "energy" can be represented in a formula that connects mass
and velocity in order to determine it. For Newton energy was represented as a "momentum" or
massxvelocity and not as a "vis-viva" as mass velocity squared as Leibniz understood it [it wasn't until a
hundred years later that a French aristocratic lady named L'Chatelet explained this to us.


In Galileo's age, space itself was not represented in the calculations using coordinate axes and vectors
in space as we do now. Although the beginnings of perspective and projections were beginning to be
studied geometrically by Renaissance artists, the differences between what we now call metric
projective geometry and metric Euclidean geometry were not understood. Space itself was considered
only a place or location for objects and our sense impressions of them. The concept of what we now
call in mathematical physics of a manifold [a collection of places for objects and our thoughts about
them, not all of which are sense impressions but which can be studied mathematically]. This requires
the notion of what a collection or sets of objects are. Also, the idea a ‘field’ of locations or places for
objects and our thoughts about them [requiring for its final definition a better understanding of what a
motion is and what a ‘force’ is] was not understood. Galileo went back to Aristotle and improved on his
method of using conservation of momentum to solve problems in physics. He used a two dimensional
scheme of how vertical and horizontal axes are balanced geometrically to represent velocities and
accelerations in a geometrical wau of visualization that helped solve problems in the displacement of
water volumes by ships and trajectories of falling bodies fired from cannons.
Only later were Newton, Descartes, Riemann, Weierstrass building on their study of Galileo’s
discussions and dialogues about how these ideas are to be defined outside of a context of theology but
within one of science and logic was modern mathematics and physics able to accomplish all it has.
Aristotle being one of the best human philosphers and logicans that has ever existed, he had confused
everybody, about the nature of space and motion (which affects how we think we can visualize temporal
and eternal spiritual beings with our souls).
We now consider Galileo and not Aristotle right as to whether bodies can move from there own nature
{they can’t}. Most people now would say that bodies do not have a separate ‘nature’ such as a
consciousness. But, the answer to this question depends on how we define ‘bodies [matter]’ and
‘nature’. If we are metaphysical ‘dualists’ and separate everything into ‘body’ and ‘mind’ and ‘spirit’,
then the mind is considered separate because it is capable of having ‘consciousness’ of which is
something that is capable of having ‘intentions’.
“A spirit is defined as something as not being composed of ordinary ‘material’ things and not subject to
‘ordinary material’ laws. Ordinary matter being composed as we know of something that has the
qualities of ‘mass’, ‘volume’,’velocity’,’solidity’.
Ordinary material laws referring to the laws of physics as we currently understand them. Light, for
instance, is not composed of ordinary matter. But, its behavior does compose to ordinary physical laws.
And, we know from the laws of quantum mechanics that it can exist in different ‘states’ or ‘quantum
levels’ corresponding to the frequency of how it vibrates the ‘space’ it is existing in. It is therefore not
spiritual. Neither is a magnetic field. “
Keith Campbell “Body and Mind”.

And, to our friend, professor Einstein and Michael Faraday, and James Clerk Maxwell we owe the idea
that the "vis-viva" formula for energy, the mass of an object [possibly atomic like a light photon], and its
speed can be connected all together in the wonderful expression E = m x c^2.
Is there some way that a generalized understanding of what "motion" is can also be generalized to a
better understanding of what the other two concepts, that of mass, and that of velocity squared, are in
the above equation? Modern day mathematicians and physicists are nowadays trying to do this using an
idea of expressing the formula for this in terms of what is called a "Lagrangian" on a "vector bundle" [or
some other algebraic geometric type of space]. All this is still very much up in the air and subject to
change because we don't understand what the concept of "dark energy" or "dark matter" is that we are
trying to find in order to make our astronomical observations come up right. And, if you add the possibly
that the type of mental "psychic" motion we are discussing might require a new definition of what
"mass" is we are really confused. Such a space that we have been talking about algebraically would
probably have what we call non-commutative motion. And, geometrically, to have to have some "metric"
structure would entail having attached to it what we call a "quadratic form" [possibly a form calculated
over not just the real numbers, but the complex, or quaternions, or octernions], or Cayley numbers".
But, we would also need a way of reducing the number of possibilities of such forms [either by
experiment or considerations of combinatorial symmetry of space translations and tilings] in order to
determine which unique solution among the many possibilities God had to choose.

For one interesting method to combine the algebra, the geometry, of the space translations and tilings
of quadratic forms see my 1974 UC Berkeley Mathematics Thesis " VoronoiReduction of Quadratic
Forms".


God, of course, assuming He exists, as we do, because He is omnipresent has the qualities of both
existing in space [being a body] and because He is omnipotent, of having consciousness and intentions
[having a mind.], and not being composed of ordinary ‘material’ things and not subject to ‘ordinary
material’ laws [ He is omnipotent, being a Spirit even a self-existing One composed of the nature of
‘Oneness’ or so we believe through faith].


As our friend Dante, as discussed in this blog above, has explained because we have ‘Hope’ in God we
have the ‘Certain expectation of future glory’. We have a ‘Certain’ sense of Hope in this in the sense
that I have discussed how our friend Pascal defined Hope more precisely for this a century later when
he created the mathematical area of what we now call Probability Theory. In these realms we are
dwelling as a result of our own free will and His saving, redeeming, sanctifying, justifiy grace with Him.
We are dwelling in different levels in these realms of Heaven, Earth, Heaven or Earth, Heaven and Earth
in some sense which we can have visions of like Dante but it very hard to define using the laws of
science. The realm of ‘Earth’ is the realm of material Oneness, the realm of One substance which our
bodies which occupy ‘one’ material space live and realize our hopes and dreams in the past, present,
and future with God’s help.